We use the package micrOMEGAs [1]} to accurately calculate the relic abundance \(\Omega _H\)  in the above parameter space, including all possible annihilations and co-annihilations. When \(M_H\)  approaches the half of the SM Higgs mass \(M_h/2\simeq 62.5\,{\rm GeV}\)  [2]}, [3]}, the Higgs resonance in the \(s\) -channel would become prominent, which is characterized by the coupling \(\lambda _L\)  controlling the trilinear vertex \((\lambda _L v)hH^0H^0\) . However, in other regions, the DM annihilation cross section is dominated by the \(WW^{(*)}\)  mode. Therefore, the correct DM relic abundance is achieved mainly by the balance of the \(WW^{(*)}\)  and Higgs resonance channels. Fig. REF  shows the relevant parameter space in the \(M_H\) -\(|\lambda _L|\)  plane, which can give the observed DM abundance \(0.112\lesssim \Omega _H h^2\lesssim 0.128\)  at \(3\sigma \)  level [4]}, [5]}, [6]}. Note that when DM is heavier than 73 GeV, the \(WW^{(*)}\)  channel would give a too large annihilation cross section to accommodate the DM relic abundance [7]}, [8]}, which is omitted in Fig. REF .
